States Definition and 1000 Threads

Consider a particle in an infinite square well described initially by a wave that is superposition of the ground state and the first excited states of the well: Ψ(x,t = 0) = C[ψ1(x) +ψ 2 (x)] (a) show that the value C =1/ 2 normalizes this wave, assuming 1 ψ and 2 ψ are themselves normalized...

Dear all, In Density Functional Theory (DFT) the Kohn-Sham eigenvalues are used to construct the band structure and the density of states (DOS). For a 3D extended system the eigenvalues are determined up to a constant since there is no absolute energy reference, while for a 2D extended...

Hi I know that stationary states in a system with an even potential energy function have to be either even or odd. Why does the ground state have to be even, and not odd? This is asserted in Griffiths, page 298.

Hi, I stumbled upon this dilemma in a homework problem which involved 2D photon gas (unphysical, I know). How many polarization states are there for EM-radiation confined to 2D? In 3D it's 2, but how does it work in 2D? An EM-wave propagating in the z-direction can have its E-component...

Homework Statement Part A) Establish which of the following combinations of particles can exist in a state of I=1 : a) \pi^0\pi^0 b) \pi^+\pi^- c) \pi^+\pi^+ d) \Sigma^0\pi^0 e) \Lambda^0\pi^0 Part B) of the problem is: In what states of isospin may exist the following systems? f)...

Homework Statement a) Enumerate the possible L and S for the 2s2p3p configuration. b) Find the possible L and S for the 2p^23p configuration. Homework Equations ^{2S+1}L_J S=0 (Singlet) S=1 (Triplet) The Attempt at a Solution First of all, doesn't "enumerate" and "find the possible...

Hello, this is quite a basic question I know, but something I'm not sure I've fully got my head around. In classical particle mechanics the dynamical variable is the position vector x, and in classical field theory the dynamical variable becomes the field \phi(x) , with x being relagated to...

How does one solve bound state problems in QFT(like an electron positron atom)? How does one identify the space of states. The Fock space seems to lose it definition when a bound state problem is discussed. There is also no meaning to wave functions or potentials that are used in standard...

Hi guys I have an analytical expression f(x) for my density of states, and I have plottet this. Now, I also have a complete list of my Hamiltonians eigenvalues. When I make a histogram of these eigenvalues, I thought that I should get an exact (non-continuous) copy of my plot of f(x). They...

What do mesocopic or even macoscopic superposition states mean? Can we look at a superposition, at a state |alive> + |dead> or |particle here> + |particle over here> ? thank you

I've been following the lectures given by Leonard Susskind on Quantum Entanglement. In Lecture 6, he describes a simplified version of the two-slit experiment so that we can use finite dimensional spaces to describe the system (which is all we've learned so far). He also uses what he calls...

Say you have a Yukawa potential (a.k.a. screened coulomb potential) V(r) = -\frac{e^2}{r}e^{-rq} where q is the inverse screening length, how would you find the critical q for having bound states? I'm working on reproducing N.F. Mott's argument about the critical spacing of a lattice of...

Hi guys I found this on Google Books...

Hi everyone, A QM question that I am stuck on: Consider the addition of the spin of 2 electrons, s1=s2=½. Show that there are one ms=1; two ms=0 and one ms=-1 states. Show the 4 spin states are given by: a1a2 b1b2 (1/(sqrt(2)))(a1b2+b1a2) (1/(sqrt(2)))(a1b2-b1a2) I've used a...

In a system with two spin 1/2 particles , We now ask what are the allowed total spin states generated by adding the spins ${\bf S}= {\bf S}_1 + {\bf S}_2$ ,in fact, they are Singlet and Triplet Spin States \left( \begin{array}{ll} |1,1\rangle & =\uparrow\uparrow\\ |1,0\rangle &...

Homework Statement Consider an isolated system consisting of a large number N of very weakly interacting localized particles of spin 1/2. Each particle has a magnetic moment \mu which can point either parallel or antiparallel to an applied field H. The energy E of the system is then E =...

i have an equation for the density of states that depends on 1/(sqrt E). i have lots of coefficients to this [Vm^{3/2} w_c ] / [2 sqrt {2} pi^2 hbar^2] do these coefficients represent the degeneracy of the desity of states?

i'm given either |0> or cos\phi|0> + sin\phi|1> by a fair coin toss. and I don't know which state I'm given. i need guess which state was chosen. i think the method is to do a unitary operation on the states, and do the measurement, but I'm not sure how to construct a unitary, and I'm still...

Hi. I'm studying the transition rates between a state a and a state b in the continuos level. In the book "Physics of atoms and molecules" by Bransden and Joachain it is said: We have to calculate the density of final states. To do this let the volume V be a cube of side L. We can impose...

I have a question regarding the possible oxidation states of metals. I understand how to find the oxidation state of a metal in a compound, that's pretty straightforward. What I'm interested in is finding possible oxidation states given only the name of the metal. For example, Cu has possible...

In terms of stationary states we have bound states and free(plane wave or Coulomb) states Autoionizing states are free(E>0), e.g. continuum, but localized states(resonances). Hence wavepackets consisting of a band of plane or Coulomb waves. I understand they may be long-lived, longer than the...

i was looking at the number line and its various axis and thought, this is a system for storing states of energy. whereupon when we input figures we actually send a quantified amount of energy into the network and the energy is bounce around according to the resistance it meets within the system...

Homework Statement The ground state of _{6}Cl^{13} has spin-parity 1/2- and the next three excited states have values of 1/2+, 3/2- and 5/2+. Explain these values in terms of the shell model.The Attempt at a Solution The problem is that i don't know what is being asked of me...i initially...

The multiverse theory states that there are an infanite amount of other realities, and that anything that can happen will hapen. How does this really work?

Anyone know the difference between how electron fill the orbitals as opposed to nucleons. And what are the special properties of systems with closed shell characteristics.

Hi, I am trying to find an expression for the density of states of free two-dimensional electrons, as a function of energy, and I am really struggling. I get that what I am looking for is the number of states per unit area of k-space per unit energy, and in general (3D), this is expressed as...

Let's say you have some quantum particle whose eigenvalues for some observable Q are either degenerate or non-degenerate. If you measure the observable and find it to be in a non-degenerate state, then you know that the wave function has collapsed onto this state. Now if you measure the...

I understand that all real-world applications can never attain 100% efficiency, whether it be referring to something mechanical, electrical, or some thermodynamic cycle. While studying the Carnot cycle and learning about the upper limit of efficiency for thermodynamic cycles, I drew a blank...

Hi, I have a question about statistical mechanics. How do you calculate the density of states for phonons and electrons in a d-dimensional system (at fixed chemical potential) and when the dispersion relation for the electrons is E(p)=A |p|^g and for the phonons is w=v|p| To get the...

Is it perpetual? I think it will continue to be very large because the US is top dog. How many nations are likely to ask the US for their money back, and what could they possibly do to warrant the US to pay up? People seem to like our money, so why not share?

Why the term "cylindrical functions" for the states in LQG? I just can't find a any reference that explain the why of the term "cylindrical" for the states in LQG. Thanks in advance for any comment. Z.

in the below question are 2 identical, homogeneous boards, glued together at their centres with the forces applied as in the diagram. the maximum normal stresses are 30MPa for the boards and 20Mpa for the glue the maximum shear stresses are 10MPa for the boards and 10Mpa for the glue the line...

hi could someone please verify that my calculated probability for superposition of states is correct (i derived it myself from a simpler equation) where \Psi=c1\psi1 e^{-iE1t}+c2\psi2 e^{-iE2t} and \psi_i, c_i \in \mathbb{R}...

say we had two states \psi1 and \psi2 and i want to model the superposition of the two states \psi=c1\psi1+c2\psi2. how do i find c1 and c2? I've been trying to do c1=\int\psi \psi1 r^2dr over the limits 0 and infinity but i don't seem to be getting anywhere. does anyone have any ideashow i...

How do you find the scalar product of two non-orthogonal many particle states? For example <\leftarrow,\rightarrow|\uparrow,\downarrow> I wanted to express both as a 4-vector in the up/down basis, but this seems weird, since then a state |\uparrow\downarrow+\downarrow\uparrow> is like...

Quantum - Projection Probability - "Projection amplitudes for SHO states." Given the two normalized 2D SHO wave functions <x,y|mx[/SUB ],ny> for the second energy level n = nx + ny = 1 in the m[SUB]x[/SUB ],n[SUB]y representation: <x,y|1,0> = (2/pi)1/2xexp[-(x2+y2)/2] <x,y|0,1> =...

Sorry for a (maybe) dumb question, but... I understand that according to QM, the description of the situation for a particle or system is described by a linear superposition of the wave functions of all the possible states (eigenstates) of the system. When a measurement is made, the wave...

Ex-DEA agent Celerino Castillo exposes the atrocities and drug smuggling involvement of the US government: http://www.youtube.com/watch?v=udDPdZ48JMs&feature=related

I have a graph where from each node the state can change randomly from one node to some of the other nodes. My task is to estimate how long the state will stay within a subset of all these nodes. Is there a way to characterize the network with some parameters to find the answer (maybe for a...

This is not a homework problem, just a question I encountered I thought I should figure out. Homework Statement ....__... _______ ..._____...|..|_ ..|-------------Energy ....|_|...|_| ...A...B.C.D..E...FEdited due to formatting of my picture. Please ignore the periods I had to use them to...

Homework Statement Suppose we define states [0] and [1] be the basis which [0] = (1,0) and [1] = (0,1). There are two things I want to ask. Are the following states product or entangled states? (i) [Xi] = \frac{1}{2} ([00] + [01] + [10] - [11]) (ii) [Xi] = \frac{1}{\sqrt{10}} ([01]...

Hello, is it possible to roughly estimate the density of states just looking at the band structure E(k) of a solid? Thanks

Litium has a structure 1s^22s^1 What is the first exited state of litium? I have some doubt? I think that it is 1s^22p^1 Is it correct or maybe 1s^23p^1 Why I'm in problem. Because wave function of hydrogen atom depends of three quantum numbers \psi_{n,l,m} but energy...

Let’s say i have n identical classical non interacting particles and N sites where i can put them in. BUT the total energy is given. The number of possible states is (N)^n/n!/(n/2)! Where N^n is the total possibilities to arrange the particles. We divide it by n! since they are identical...

In molecular orbital theory, there are two molecular states. (see below) I don't know the differences between these two states?

Homework Statement Which of the following states have odd parity? a. 2p m=0 b. 2p m=1 c. 26f m=0 d. 2s The Attempt at a Solution Knowing the wavefunctions for a,b, and d, i think that all of them have odd parity. What about the 26f m=0 state?

Hey, My brain seems to have shut down. Let's say I'm working in the space H_a \otimes H_b and I have an operator A and B on each of these spaces respectively. Furthermore, consider a general state in the tensor space |\psi \rangle = | x_1 \rangle |y_1\rangle + |x_2 \rangle |y_2 \rangle...

Hello, 1)Why does the number of helicity states depend on space-time dimension ? Masselss graviton in 4 dimensional space has 2 helicity states ( 2 degrees of freedom). In 5 dimensional space it has (still massless in 5 D) 5 helicity states (5 degrees of freedom) ... In 6 dimesional...

Someone reopened an old thread which had devolved into mud slinging but it made me think. Is it possible to move power to the individual states/ This is the same problem facing the EU but from the other side - in the eu all new rules eg. to remove trade barriers, seem to lead to a more...

I'm reading through the Introduction to Quantum Mechanics book by Griffiths (2nd edition) and it is describing delta-function potential wells. When it describes how to find bound states the energy is E < 0 (negative) in the region x < 0 (negative). It says the general solution is: \psi (x)...